What is a normal and what is a tangent?

The law of normal mainly refers to rules, laws, standards, and alignments.

A line that satisfies a certain rule is called a normal in a specific field;

Normals are defined differently in different areas, i.e. there are many types of normals.

For example, the rule of light reflected by a plane mirror satisfies that the angle of incidence is equal to the angle of exit; The line perpendicular to the reflective surface and passing through the point of incidence is the normal;

If it is a concave mirror or a convex mirror, it is the perpendicular line of the tangent plane of the incident point (also passing through the incident point);

In analytic geometry, there is a normal for the tangent of the curve, that is, the straight line perpendicular to the tangent is the normal (this concept is used for specular reflection).

In solid geometry, there are normals and normals for planes, and the normals are vectors with a length unit of 1 in the vertical direction of the plane; A normal is a straight line (the line is perpendicular to the plane) along a normal vector at a certain point;

Tangent. Geometrically, a tangent is a straight line that touches a point on a curve. More precisely, when a tangent passes through a point on the curve (i.e., a tangent), the direction of the tangent is the same as that point on the curve, and the "part of the tangent near the tangent" is closest to the "part of the curve near the tangent" (infinite approximation idea).

Tangent means "to touch" in Latin. Similar concepts can also be generalized to concepts such as plane tangent.

Definition of curve tangents and normals.

p and q are two adjacent points on the curve c, p is the fixed point, when the q point is infinitely close to the p point along the curve c, the limit position pt of the secant pq is called the tangent of the curve c at the point p, and the p point is called the tangent point; The straight line pn that passes through the tangent point p and is perpendicular to the tangent pt is called the curve c at the normal of the point p (the idea of infinite approximation).

Note: In plane geometry, a straight line with only one common intersection point with a circle is called a tangent of a circle, and this definition does not apply to general curves; pt is the tangent of the curve c at the point p, but it has another intersection with the curve c; Conversely, the straight line l, although it has only one intersection with curve C, is not a tangent of curve C. ．

A normal is a straight line perpendicular to a plane or curve tangent, and a tangent is a straight line perpendicular to the radius of a circle and has only one intersection point with the circle.

A straight line perpendicular to the radius and passing through the tangent is a tangent.

A straight line where the tangent is perpendicular to the tangent is normal.

Tangent: A line has a common point with a circle.

The product of the slope of the normal and the slope of the tangent is -1, and the tangent equation representing the curve y=f(x) at the point m(x0,y0) is expressed as a derivative: y-f(x0)=f'(x0)(x-x0)。The product of the slope of the normal and the slope of the tangent is -1, and the normal can be expressed by a one-dimensional equation, which has a conversion relationship with the derivative.

The tangent equation for the curve y=f(x) at the point m(x0,y0) is expressed by the silver conduction withering number: y-f(x0)=f'(x0)(x-x0) The equation for the line is: y-f(x0)=(1 f'(x0))*x-x0)。

Definition of tangent: Geometrically, a tangent refers to a straight line that just touches a point on a curve.

tangential sentences; 1. It includes basic elementary geometry, conic curves, geometric functions, and tangent curves.

2. The tangent stiffness matrix of geometric nonlinearity is deduced from the engineering strain, and the criteria for judging the divergence point and the limit point are given, and finally the analysis process of the method is illustrated with a numerical example.

3. This definition assumes some expressions of the subtangent.

4. Departure angle: the tangent line of the rear end protrusion point of the car to the rear wheel and the angle between the ground.

5. After the rotation, the direction of movement is from south to north, which is also a tangent motion along the circumference.

6. In the scope of projective geometry, the common point of the biquadratic curve and the problem of the common tangent line are comprehensively discussed.

7. The programmer must provide the tangent, subnormal, and normal of each vertex.

8. This section covers how to animate curves directly in the animation view. These include efficient navigation, creating and moving keyframes, and tangent and tangent types.

9. This data can be used to create a rotation matrix for each vertex on the surface, which can be used to convert vectors from a global coordinate system to tangent space.

10. The oblique cutting knife can cut the paper obliquely. Its tangent line is at an angle to the direction of the paper grain.

11. But I naively chose a college that was as expensive as Stanford, and my working-class public cut spent all my savings on my college tuition.

12. No tumor was found in the "upper, lower, anterior, posterior, and bottom tangents" sent for examination.

13. Life is a circle, some people have walked all their lives and have not walked out of the circle drawn by fate, he just doesn't know that every point on the circle has a tangent line that takes off.

Due to tangents. Perpendicular to the normal, so the slope of the tangent is multiplied by the slope of the normal = -1. i.e. slope k=tan , inclination angle.

k1*k2=tanθ*tan(θ+90°)=tanθ*(cotθ)=1。

Geometrically, a tangent is a straight line that just touches a point on a curve. More precisely, when a tangent passes through a point on the curve (i.e., a tangent point.

, the direction of the tangent is the same as the direction of the point on the curve. In plane geometry, a straight line that has only one common intersection with a circle is called a tangent of a circle.

Normal, a dashed line that is always perpendicular to a plane. The normal of a curve is a straight line perpendicular to the tangent of a point on the curve, and the normal of a point on the surface is the straight line (i.e., the vector) that passes through the point and is perpendicular to the tangent plane of the point.

In physics, a straight line with the point of incidence perpendicular to the mirror is called a normal.

For a solid surface, the normal is directional: the positive direction of the normal is destroyed by the inside of the solid surface to the outer segment, and the negative direction of the normal is reversed.

Geometrically, a tangent is a straight line that touches a point on a curve. More precisely, when a tangent passes through a point on a curve (i.e., a tangent point), the direction of the tangent filial piety line is the same as the direction of that point on the curve. In plane geometry, a straight line that has only one common intersection with a circle is called a tangent of a circle.

In advanced mathematics, for a function, if there is a derivative somewhere in the function, then the derivative here is the slope of the tangent that crosses there, and the straight line formed by the point and the slope is a tangent of the function.

Main nature. 1) Tangents and circles have only one common point;

2) The distance between the tangent and the center of the circle is equal to the radius of the circle;

3) the tangent is perpendicular to the radius passing through the tangent point;

4) A straight line perpendicular to the tangent line through the center of the circle must pass through the tangent point;

5) A straight line perpendicular to the tangent must pass through the center of the circle;

6) The tangent and secant line of the circle from a point outside the circle, and the tangent length is the middle term of the ratio between this point and the length of the two line segments between the midline and the intersection of the circle.

A tangent line (pronounced qiē xiàn) is a straight line that just touches a point on a curve. More precisely, when a tangent passes through a point on the curve (i.e., a tangent), the direction of the tangent is the same as that point on the curve, and the "part of the tangent near the tangent" is closest to the "part of the curve near the tangent" (infinite approximation idea). Tangent means "to touch" in Latin.

Similar concepts can also be generalized to concepts such as plane tangent.

Geometric definitions of curve tangents and normals.

p and q are two adjacent points on the curve c, p is the fixed point, when the q point is infinitely close to the p point along the curve c, the limit position pt of the secant pq is called the tangent of the curve c at the point p, and the p point is called the tangent point; The straight line pn that passes through the tangent point p and is perpendicular to the tangent pt is called the curve c at the normal of the point p (the idea of infinite approximation).

Note: In plane geometry, a straight line with only one common intersection point with a circle is called a tangent of a circle, and this definition does not apply to general curves; pt is the tangent of the curve c at the point p, but it has another intersection with the curve c; Conversely, the straight line l, although it has only one intersection with curve C, is not a tangent of curve C.

Algebraic definitions of curve tangents and normals.

In advanced mathematics, for a function, if there is a derivative somewhere in the function, then the derivative here is the slope of the tangent that crosses there, and the straight line formed by the point and the slope is a tangent of the function.